Problem: Solve for $x$. $3^{10}=3^7\cdot x^3$ $x=$
Explanation: When powers have the same base, $x^m\cdot x^n=x^{m+n}$. Let's expand the powers for ${3^{10}}={3^7}\cdotx^3}$. $\begin{aligned} &={\underbrace{3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3}_\text{7 times}}\cdot\underbrace{x\cdot x\cdot x }_\text{3 times}} \\\\\\ &={\underbrace{3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3}_\text{10 times}} \\\\ \end{aligned}$ $x=3$